Table 7 Coefficients of the PDF, the MGF and the BEP for the upper and the lower bounds of BD

$\frac{{\lambda }_{\text{RD}}}{3}\sum _{k=2}^N{c}_k{(1-\beta )}^{k-1}\left(\frac{1-\beta }{k-\frac{4}{3}}+\beta \right)$

$c_4{(1-\beta )}^3\beta {\lambda }_{\text{RD}}+{\lambda }_{\text{RD}}\sum _{\underset{k\ne 4}{k=2}}^N{c}_k{(1-\beta )}^{k-1}\left(\frac{1-\beta }{k-4}+\beta \right)$

-

$\frac{c_4{(1-\beta )}^4{\lambda }_{\text{RD}}^2}{4}$

$\frac{c_k{(1-\beta )}^k{\lambda }_{\text{RD}}}{4}\left(1-\frac{k}{k-\frac{4}{3}}\right)$

$\frac{c_k{(1-\beta )}^k{\lambda }_{\text{RD}}}{4}\left(1-\frac{k}{k-\frac{4}{3}}\right),k\ne 4$

$\frac{3}{2{\lambda }_{\text{RD}}}\left(\frac{2A^{\left(S\right)}{\lambda }_{\text{SD}}}{\frac{-2{\lambda }_{\text{RD}}}{3}+{\lambda }_{\text{SD}}}\right)$

$\frac{1}{2{\lambda }_{\text{RD}}}\left(\frac{2A^{\left(S\right)}{\lambda }_{\text{SD}}}{-2{\lambda }_{\text{RD}}+{\lambda }_{\text{SD}}}-\frac{4B^{\left(S\right)}{\lambda }_{\text{SD}}}{{(-2{\lambda }_{\text{RD}}+{\lambda }_{\text{SD}})}^2}\right)$

-

$\frac{1}{4{\lambda }_{\text{RD}}^2}\left(\frac{4B^{\left(S\right)}{\lambda }_{\text{SD}}}{-2{\lambda }_{\text{RD}}+{\lambda }_{\text{SD}}}\right)$

$\frac{2}{{\lambda }_{\text{RD}}k}\left(\frac{2E_k^{\left(S\right)}{\lambda }_{\text{SD}}}{-\frac{{\lambda }_{\text{RD}}k}{2}+{\lambda }_{\text{SD}}}\right)$

$\frac{2}{{\lambda }_{\text{RD}}k}\left(\frac{2E_k^{\left(S\right)}{\lambda }_{\text{SD}}}{\frac{-{\lambda }_{\text{RD}}k}{2}+{\lambda }_{\text{SD}}}\right)$

$\frac{2A^{\left(S\right)}}{\frac{2{\lambda }_{\text{RD}}}{3}-{\lambda }_{\text{SD}}}+\sum _{k=2}^N\frac{2E_k^{\left(S\right)}}{(\frac{{\lambda }_{\text{RD}}k}{2}-{\lambda }_{\text{SD}})}+D^{\text{(DF)}}$

$\frac{2A^{\left(S\right)}}{2{\lambda }_{\text{RD}}-{\lambda }_{\text{SD}}}+\frac{4B^{\left(S\right)}}{{(2{\lambda }_{\text{RD}}-{\lambda }_{\text{SD}})}^2}+\underset{k\ne 4}{\underset{23DF}{\sum _{k=2}^N}}\frac{2E_k^{\left(S\right)}}{\frac{{\lambda }_{\text{RD}}k}{2}-{\lambda }_{\text{SD}}}+D^{\text{(DF)}}$